Remark 3.1 We remark that the use of \(\operatorname{M\ddot{o}b}^{4}\)  and \(\operatorname{M\ddot{o}b}^{8}\) 
transformations like (REF ) and (REF )
is naturally allowed since we are in the framework of the
non-autonomous CAC construction given in
[1]}, [2]}, [3]}, [4]}.
Non-autonomous Möbius transformations can be used also in
the autonomous case, see [5]}, [6]}, but
in non-autonomous case they are the natural group which
preserves the classification [7]}.

